Stress partitioning and effective behavior of N-phase laminates in anisotropic elasticity from a fast explicit method

Thiebaud Richeton (1, 2)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
2 Labex DAMAS

In this work, a fast explicit method, easy to implement numerically, is proposed in order to compute the effective behavior and the distribution of stresses in a general N-phase laminate made of parallel, planar and perfectly bonded interfaces. The solutions are exact for a homogenous far-field loading and work for an arbitrary number of phases, a general linear anisotropic elasticity, as well as different uniform thermal and plastic strains in the phases. A simple direct analytical formula is also derived to compute the stress in a given phase once the effective behavior of the laminate is known. Moreover, the correctness of the proposed method is checked by comparisons with finite element simulation results on a same boundary value problem, showing excellent agreements. An application of the method is performed for a near-$\beta$ titanium alloy with elongated grains, by comparing the level of internal stresses for different elastic loadings within a N-phase laminate made of $100,000$ orientations and a 2-phase laminate of equal volume fraction with maximal elastic contrast. Interestingly, the maximum von Mises stress of the 2-phase laminate is always the lowest, which is explained by a volume fraction effect. Finally, comparisons with elastic self-consistent models considering oblate spheroidal grains of different aspect ratios are performed.

Mots clés: laminate; anisotropic elasticity; incompatibility stresses; effective behavior; composite structure

Domaines: Mécanique [physics.med-ph]; Matériaux; Mécanique [physics]

Thiebaud Richeton. Stress partitioning and effective behavior of N-phase laminates in anisotropic elasticity from a fast explicit method. 2021. ⟨hal-03347969v2⟩